Molecular Systems Biology 8; Article number 610; doi:10.1038/msb.2012.42 Citation: Molecular Systems Biology 8:610 & 2012 EMBO and Macmillan Publishers Limited All rights reserved 1744-4292/12 www.molecularsystemsbiology.com

Gene location and DNA density determine transcription factor distributions in Escherichia coli Thomas E Kuhlman1,2,* and Edward C Cox1 1

Department of Molecular Biology, Princeton University, Princeton, NJ, USA and 2 Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA * Corresponding author. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801, USA. Tel.: þ 1 858 531 4386; Fax: þ 1 217 244 7187; E-mail: [email protected] Received 16.3.12; accepted 9.8.12

The diffusion coefficient of the transcription factor LacI within living Escherichia coli has been measured directly by in vivo tracking to be D ¼ 0.4 lm2/s. At this rate, simple models of diffusion lead to the expectation that LacI and other proteins will rapidly homogenize throughout the cell. Here, we test this expectation of spatial homogeneity by single-molecule visualization of LacI molecules non-specifically bound to DNA in fixed cells. Contrary to expectation, we find that the distribution depends on the spatial location of its encoding gene. We demonstrate that the spatial distribution of LacI is also determined by the local state of DNA compaction, and that E. coli can dynamically redistribute proteins by modifying the state of its nucleoid. Finally, we show that LacI inhomogeneity increases the strength with which targets located proximally to the LacI gene are regulated. We propose a model for intranucleoid diffusion that can reconcile these results with previous measurements of LacI diffusion, and we discuss the implications of these findings for gene regulation in bacteria and eukaryotes. Molecular Systems Biology 8: 610; published online 11 September 2012; doi:10.1038/msb.2012.42 Subject Categories: chromatin & transcription; microbiology & pathogens Keywords: facilitated diffusion; genome organization; single molecule microscopy; transcriptional regulation

Introduction Regulation of gene expression by the binding and unbinding of transcription factor proteins (TFs) at specific regulatory sites in response to environmental stimuli is the fundamental mechanism organisms use to adapt to changing environments. An understanding of how TFs search for and find their binding targets is thus of fundamental importance if we are to understand the design and behavior of genetic circuits and their components (Gerland et al, 2002). The seminal theoretical and in vitro work of Berg, Winter, and von Hippel forms the basis for our current understanding of the TF search mechanism known as facilitated diffusion: TFs are thought to bind non-specifically and slide in one dimension along the DNA, in addition to three-dimensional diffusion throughout the cytoplasm (Berg et al, 1981; Winter and von Hippel, 1981; Winter et al, 1981). Recent studies of the lac repressor, perhaps the best-studied transcription factor in E. coli, have revealed that diffusion of repressor in live cells is rapid, of order DB0.4 mm2/s (Elf et al, 2007). At this rate, a single molecule travels the length of E. coli in 1–10 s, and simple models reveal that the distribution of repressor should be homogeneous throughout the DNA and cell. Here, we test this expectation by using high-throughput single-molecule microscopy to determine the average spatial distribution of lac repressor, LacI, in a strain deleted for the native lac operon. Because these strains lack a specific binding & 2012 EMBO and Macmillan Publishers Limited

target, we can ask if the theoretical expectation of uniform distribution along the DNA and in the cytoplasm is met. Surprisingly, we find that the distribution is inhomogeneous and dependent on the location of the repressor gene, showing that our current understanding of the search process is far from complete. We further show that this inhomogeneity is the result of competition between non-specific DNA binding on the one hand and exclusion of the repressor from DNA on the other hand. Finally, we show that this inhomogeneity can be detected as stronger repression of targets located near the TF gene than would be expected from a homogenous repressor distribution, and we discuss the implications of these findings for gene regulation and the evolution of genome organization.

Results To visualize the spatial distribution of non-specifically bound lac repressor molecules, we integrated a gene encoding LacI fused to the fluorescent reporter Venus at four different chromosomal locations in a strain where all lac repressor binding sites have been deleted (Kuhlman and Cox, 2010). These sites were near the replication origin of the circular genome, near the replication terminus, or halfway between the origin and terminus on the right or left halves of the chromosome, or replichores (Supplementary Figure 1A), and particular care was taken not to include any pseudooperators Molecular Systems Biology 2012 1

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

overlapping the 30 end of either lacI or venus (Oehler et al, 1990, 1994; Mu¨ller-Hill, 1998; Elf et al, 2007). These strains were grown to exponential steady state (Supplementary Figure 2), fixed with paraformaldehyde, and imaged to determine the spatial distribution of non-specifically bound LacI-Venus molecules using total internal reflection fluorescent (TIRF) microscopy, the distribution of DNA using staining with 40 ,6-diamidino-2-phenylindole (DAPI), the location of the lacI-venus integration sites determined by the fluorescent reporter-operator system (FROS; Joshi et al, 2011), and the corresponding lacI-venus mRNA distributions determined by fluorescence in situ hybridization (FISH; Raj et al, 2008; So et al, 2011). We took B1000 images for each strain and growth condition. We then used an automated cell-finding algorithm to identify individual cells in each image, binned cells by size, and averaged the fluorescent intensity at each pixel to determine the average spatial distribution of each component (Figure 1). Due to hardware limitations, we were unable to dynamically switch between epifluorescent and TIRF illumination, and this limitation precludes the simultaneous highthroughput measurement and direct correlation of gene location and protein distribution in the same cell. Consequently, imaging of the spatial distribution of each component

A

B

r

C

θ y x

200

Count

150 100

(DNA, gene, mRNA, and protein) was performed in separate measurements. The absolute orientation of each cell is then ambiguous, and we additionally perform an average over all possible orientations, which introduces symmetries into the resulting average distributions.

Repressor gene location influences TF distributions The average distributions of DNA, lacI-venus gene location, lacI-venus mRNA, and LacI-Venus protein for cells that have just divided are shown in Figure 2. We find that the replication origin-proximal integration locus is located midcell and the terminus-proximal locus at a superposition of the poles and midcell (Bates and Kleckner, 2005; Wiggins et al, 2010). These results are in broad agreement with the existing literature (Niki et al, 2000; Wang et al, 2006; Montero Llopis et al, 2010; Wiggins et al, 2010). FISH reveals lacI mRNA to be localized at the gene loci for origin and terminus integrants (Montero Llopis et al, 2010). When the lacI source gene is located on a medium copy number plasmid localized to the poles (Figure 2, second column), lacI-venus RNA shows some tendency to redistribute to other locations in the cell and LacI-Venus is evenly distributed throughout the nucleoid. When the source is located within the chromosome, however, we find that the distributions depend on the position of the encoding gene on the chromosome, and correlate with the spatial distributions of the source genes. Recalling that these strains are deleted for specific LacI binding targets, interpretation of the LacI-Venus distributions for origin and terminus integrants is straightforward: when the source is near the origin, the gene, mRNA, and protein map to that location. When the source gene is integrated at the terminus, the average gene location shifts toward the poles, and the LacI distribution changes correspondingly. Furthermore, the LacI-Venus molecular phenotypes depend on the LacI DNA binding domain. LacI-Venus strains with insertions at the same locations but deleted for first 42 base pairs of the lacI coding sequence (the 14 amino acid residues of the DNA binding domain; henceforth referred to as LacI42-Venus) show that, in the absence of the DNA binding domain, the LacIVenus distributions at the origin and terminus alter dramatically (Figure 2, last row).

50

DNA density affects TF distributions 0

2

4

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D +

8 10 12 14 Cell size (length/width) +

+

Figure 1 Image averaging procedure. (A) A representative image field with lacI-venus integrated near the origin (atpI locus) imaged at  133 magnification. (B) Individual cells are found using an automated algorithm, and coordinates are established at the cellular centroid to measure cellular dimensions and the location of each pixel. (C) Because of the narrow distribution of cell widths, correctly identified cells are identified according to correspondence with the appropriate width and binned according to the ratio of the length to width. Alternating gray and white bars indicate each bin. (D) Cells within each bin are rescaled to the size of the average cell within that bin and averaged together on a per-pixel basis and over all orientations. 2 Molecular Systems Biology 2012

E. coli changes its morphology and the gross compaction state of its nucleoid in response to changing growth conditions. We assayed the spatial distribution of LacI-Venus in a variety of growth states to determine whether these changes in the intracellular environment affect the steady-state distribution of LacI-Venus protein. The results for cells containing an equal total amount of DNA in different growth states are shown in Figures 3 and 4. When bulk growth is arrested in stationary phase cells generally contain a single chromosome, are morphologically small, and the DNA is densely packed (Figure 3, second column; Supplementary Figure 3). As the growth rate increases, cells become larger and the DNA becomes more loosely packed (Figure 3, third column; Supplementary & 2012 EMBO and Macmillan Publishers Limited

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

DNA Extrachromosomal plasmid

Origin

Terminus

lacI::venus Gene

lacI::venus mRNA

LacI-Venus protein + DNA binding domain

2× 1.5×

LacI42-Venus protein – DNA binding domain

Mean 0.67× 0.5× 1 μm

Figure 2 Average spatial distribution of lacI-venus expression. Cells were grown in M63 minimal medium þ 0.5% glycerol before fixation. Averages are for cells of 1.9–2.2 mm in length, the bin identified in Figure 1D. Averages are also taken over all cell orientations, resulting in the symmetry of each plot. Raw images of combined transmitted and fluorescence channels are shown in the first column for DNA (  400, DAPI staining; row 1), gene locus (  400, FROS; row 2), mRNA (  400, FISH; row 3), LacI-Venus protein (  400, TIRF microscopy, row 4), and LacI-Venus protein without DNA binding domain (  400, TIRF microscopy, row 5). Representative LacI-Venus images are at  133magnification for visual clarity. Remaining columns show average distributions for each component with the lacI-venus source gene expressed from the indicated location. Fluorescent intensity is normalized to the mean fluorescence within the cell. The quantitative color scale is for LacI-Venus only; other averages are qualitatively scaled for comparison. The essQ locus was the LacI-Venus source for terminus, but the gene location shown is for the adjacent nth terminal locus for clarity (Kuhlman and Cox, 2010); essQ localization is identical but less clear due to reduced binding at that locus.

Figure 3). As cells reach their maximum growth rate of B20 min/doubling they contain at least two or more complete sister chromatids (Figure 4, third column; Supplementary Figure 3), and the trend of DNA decondensation in fast growing cells continues compared with slower growing cells late in the life cycle which also contain two complete sister chromatids (Figure 4, second column). It is possible that the more diffuse distribution of DNA in fast growing cells shown in Figure 4 is an artifact of image averaging: if the spatial positioning of condensed DNA within the larger volume of fast growing cells is highly variable, yet dense, averaging will make the resulting distribution appears less dense than each individual nucleoid. We therefore also quantified the compaction density of nucleoids in individual cells in each growth state by measuring the degree of geometric curvature of the DAPI fluorescent surface representing each nucleoid (see Supplementary information—Quantification of DNA Compaction). The results of this single-cell analysis are shown in Supplementary Figure 4, and demonstrate that the compaction density of DNA decreases monotonically as a function of growth rate when measured in individual cells. Measurement of LacI-Venus distributions in each of these growth states reveals that the distributions are heavily dependent on the density of the DNA. When the DNA is most highly condensed in stationary phase, LacI42-Venus appears to be generally excluded from the DNA and localized toward the ends of the cell regardless of the source location. Conversely, the pattern of localization of LacI-Venus non-specifically bound to DNA correlates closely with the location of the source gene (Figure 3, compare first and second columns). Similarly, the distribution of LacI-Venus in exponentially slow growing cells containing a single chromosome also correlates & 2012 EMBO and Macmillan Publishers Limited

closely with the distribution of its encoding gene (Figure 3, compare first and third columns). However, LacI42-Venus is no longer highly localized toward the ends of the cell and is instead more evenly distributed, although there is a weak general tendency to avoid the central nuceloid-occupied area of the cell. These subtle differences in distribution may be a consequence of different initial conditions due to different integration locations. As the cells grow and replicate their DNA, the resulting sister chromatids segregate and gene loci move around within the cell. We show in Figure 4 the distribution of LacI-Venus in slow growing (left) and fast growing (right) cells containing two complete sister chromatids. We first notice the continued apparent tendency of LacI42-Venus to avoid the central spaces occupied by the nucleoid. For the slow growing midreplichore integrants, the intact LacI-Venus distributions correlate closely with the distribution of the corresponding gene. For the origin and terminus integrants, however, the correlation is less clear. Both distributions show hysteresis: i.e., the distribution of LacI-Venus in older cells depends upon the history of the location of the gene in younger cells, in the following sense: Before replication, the origin locus produces LacI-Venus at midcell. After replication and segregation, LacI-Venus pools in the inter-chromatid space near where the origin was originally, as judged by Figures 4 and 5. Similarly, after the terminus relocates to midcell after replication and segregation, there remains a pool of LacI-Venus further out toward the ends of the cell. We propose that this tendency of LacI-Venus to pool in the nearest available space that contains less DNA is also a result of a tendency toward nucleoid exclusion of LacI-Venus molecules, and may be related to previously observed asymmetry of the cell poles (Rang Camilla et al, 2011). Molecular Systems Biology 2012 3

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

Stationary phase Minimal medium

Slow growth Minimal medium

1 μm DNA Gene location: Origin + Binding domain – Binding domain Left midreplichore + Binding domain – Binding domain Right midreplichore + Binding domain – Binding domain Terminus + Binding domain – Binding domain

Plasmid + Binding domain – Binding domain

2× 1.5× Mean 0.67× 0.5×

Figure 3 Average TF distributions as a function of growth state: one chromatid. Average DNA (first row) and LacI-Venus distributions with and without the DNA binding domain (subsequent groups of two rows, respectively) are shown as a function of lacI-venus gene integration location (rows) for stationary phase cells (left) and slow growing exponential phase cells containing one chromatid (right). Stationary phase results are from cells grown overnight in M63 minimal medium þ 0.5% glycerol. LacIVenus distributions were obtained by excitation with a 488-nm wavelength laser except in the case of the midreplichore integrants, where a 514-nm laser was used for excitation to increase the signal-to-noise ratio. The DAPI channel is shown as green in the first row to improve sensitivity to the eye. Average DNA content for exponential growth is scaled to be directly comparable to Figures 4 and 5 (see Supplementary Figure 3C and D and Kubitschek, 1974). Distributions of gene location in the first column are from cells grown in M63 þ 0.5% glycerol that are 1.9–2.2 mm in length; gene distributions in stationary phase remain similar and are compared directly in Supplementary Figure 5A.

Finally, in fast growth conditions with less densely packed DNA the distributions of LacI-Venus do not obviously correlate with the distributions of the encoding genes, nor is it obvious that the LacI42-Venus shows any tendency toward nucleoid exclusion. Furthermore, the overall absolute correlation of the LacI-Venus distribution with the DNA distribution appears significantly weaker in the fast growth state than in the slow growth state. Compare, e.g., the correlation of the distribution of LacI-Venus with the DNA distributions when LacI-Venus is expressed at high levels from an extrachromosomal plasmid in the last row in Figure 4. To further explore the influence of DNA density on the distribution of proteins, the compaction state of DNA can be 4 Molecular Systems Biology 2012

manipulated directly by adding drugs that disrupt transcription and translation (Cabrera et al, 2009). Chloramphenicol binds to the ribosome and stops peptide synthesis, and also leads to the condensation of DNA. In Figure 5A, we show the change in average nucleoid density and the resulting redistribution of LacI-Venus in exponentially slow growing cells late in the life cycle after DNA replication following the addition of 200 mg/ml chloramphenicol; cross-sections through the longitudinal axis of the distributions at time t ¼ 0 and t ¼ 10 min are shown in Figure 5B, which show the expected bilobed nucleoid structure after chromosome replication and segregation. We quantify the amount of mass displacement at each time point, D(ti), by taking the difference & 2012 EMBO and Macmillan Publishers Limited

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

Slow growth minimal medium

Fast growth rich medium

1 μm DNA

Gene location: Origin

Left midreplichore

Right midreplichore

Terminus

Plasmid 2× 1.5× Mean 0.67× 0.5×

Figure 4 Average TF distributions as a function of growth state: two chromatids. Average DNA (first row) and LacI-Venus distributions with and without the DNA binding domain (subsequent groups of two rows, respectively) are shown as a function of lacI-venus gene integration location (rows) for exponentially slow growing cells in M63 þ 0.5% glycerol (left) and exponentially fast growing cells containing two chromatids (right). Fast growth in RDM þ 0.5% glucose yields a doubling time of 22±2 min. Stationary phase results are from cells grown overnight in M63 minimal medium þ 0.5% glycerol. LacI-Venus distributions of exponentially slow growing origin and terminus integrants we obtained by Venus excitation with a 488-nm wavelength laser; all other conditions were obtained with a 514-nm laser to increase the signal-to-noise ratio. Average DNA content in each case is scaled relative to slow growing cells containing one chromatid in Figure 4. Distributions of gene location shown in the first column are from growth in M63 þ 0.5% glycerol that are 4.2–4.5 mm in length; gene distributions in exponential fast growth are similar and are compared directly in Supplementary Figure 5B.

between the initial distribution at time t0, Fðx; y; t0 Þ, and the distribution at each subsequent time point ti, Fðx; y; ti Þ, according to X  Fðxj ; yk ; ti Þ  Fðxj ; yk ; t0 Þ Dðti Þ ¼ ð1Þ j;k

The percentage of maximum displacement of both DNA (blue circles) and LacI-Venus (red circles) as a function of time & 2012 EMBO and Macmillan Publishers Limited

is shown in Figure 5C, in which we simultaneously fit both data sets to a model assuming a constant rate of displacement b, i.e., DðtÞ ¼ 1  e  bt . The simultaneous fit of both data sets to this model is shown as the black curve in Figure 5C, and we find a rate of mass displacement of b ¼ 0.60/min. Since areas of high LacI-Venus density correspond inversely to areas of high DNA density after displacement, and the displacement of DNA and LacI-Venus occurs at comparable rates, the most Molecular Systems Biology 2012 5

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

B

DNA distribution

Relative fluorescent intensity

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t=0 Add 200 μg/ml chloramphenicol t = 20 s

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100% 50% 0 0

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Figure 5 LacI redistribution as a result of nuceloid condensation. (A) The steady-state distribution of DNA and LacI-Venus in cells with lacI-venus integrated near the origin (atpI locus) and grown in M63 þ 0.5% glycerol, cell length of 4.2–4.5 mm, are shown at t ¼ 0. After this sample was taken, 200 mg/ml chloramphenicol was added directly to the culture and samples were withdrawn and fixed at the indicated times. Note that the color scale has been changed somewhat from Figure 4 to accommodate the condensed DNA. (B) Cross-sections along the longitudinal axis of the DNA (blue) and LacI-Venus (red) distributions at time t ¼ 0 (top) and t ¼ 10 min (bottom). Lines are a moving average of six adjacent points. (C) The rate of mass displacement. Displacement is quantified as the total difference between each distribution and the initial distribution at time t ¼ 0. The black line corresponds to a simultaneous fit of both data sets to the equation DðtÞ ¼ 1  e  bt . The equivalent result for LacI42-Venus is shown in Supplementary Figure 6. Source data is available for this figure in the Supplementary Information.

parsimonious explanation for these data is that the redistribution of LacI-Venus protein is driven by modifications of the DNA condensation state (see also Figures 3 and 4 and Supplementary Figure 6 for the equivalent result for LacI42Venus and Supplementary Figure 7B for similar results showing a tendency for nucleoid exclusion in response to serine hydroxamate). Nucleoid exclusion has previously been observed for large aggregates of proteins (Ebersbach et al, 2008; Winkler et al, 2010), and it is thought that exclusion may be driven by aggregation combined with entropic mechanisms (Saberi and Emberly, 2010). However, the distributions reported here are not due to LacI-Venus aggregation: expression levels from chromosomal sources are low (B1–10 molecules per cell; Gilbert and Muller-Hill, 1966), and bright spots in the images correspond to individual LacI-Venus dimers as judged by bleaching and blinking kinetics of fluorescent spots in individual fixed and living cells (Supplementary Figure 8). Furthermore, when a specific LacI binding target is present in the genome, LacI-Venus binds at the predicted location (Supplementary Figure 5D), the expected behavior for fully soluble and functional LacI dimers. The specific binding regions used in Supplementary Figure 5D are variants of the PLlac-O1 promoter (Lutz and Bujard, 1997; Kuhlman and Cox, 2010). Since this promoter binds at most two dimers and is easily distinguished using our method, this is also a 6 Molecular Systems Biology 2012

strong indication that we are imaging individual functional molecules. The patterns of localization described here do not appear to be artifacts of fixation. We show in Supplementary Figure 7A images of live stationary phase cells expressing LacI42-Venus from both plasmid and chromosomal sources, showing the same pattern of localization toward the ends of the cells reported in Figure 3, and in Figure 5 in response to chloramphenicol. We also show in Supplementary Movie 1 a movie of those cells shown in Supplementary Figure 7A with a chromosomal LacI42-Venus source that shows that the motion of LacI42-Venus molecules is severely slowed and spatially localized toward the ends of the cell. The spots shown in this movie are single LacI42-Venus molecules as determined by blinking and bleaching kinetics (Supplementary Figure 8B).

TF distributions affect gene regulation Because the strength with which bacterial promoters are regulated is a function of the concentration of the relevant transcription factors (Buchler et al, 2003; Bintu et al, 2005a, b), we next attempt to detect the local enhancement of LacI concentration near the lacI gene through the repression strength of a LacI-regulated target. We constructed three families of 14 strains where we inserted into previously & 2012 EMBO and Macmillan Publishers Limited

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

A

Origin

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oriC

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Figure 6 Repression strength as a function of intergenic distance. Repression strength as a function of genomic distance from the lacI-venus gene, where lacI-venus is near (A) origin (atpI locus), (B) mid-replichore (ybbD locus), or (C) terminus (nth locus). Red: slow growth (t ¼ 110±12 min); yellow: medium growth (t ¼ 68±5 min); green: fast growth (t ¼ 22±2 min); black: M63 þ 0.5% glycerol þ 2 mM IPTG control; circles are the mean of four measurements, error bars are the s.d. Dashed lines indicate best fits assuming spatially homogeneous distribution of repressor. Solid lines indicate best fits assuming exponential LacI-Venus inhomogeneity. Source data is available for this figure in the Supplementary Information.

constructed lacI-venus strains a cassette bearing a LacIregulated lacZ target at regular intervals around the genome (Supplementary Figure 1). In Figure 6A–C, the strength of repression is shown as a function of intergenic distance for each family of strains. Colors indicate the growth rate of the culture: slow (red), medium (yellow); fast (green); slow þ 2 mM IPTG control (black). In each plot, the x axis is adjusted so that the location of the repressor gene lies at the center of the x axis (black vertical dashed lines). In all cases, the strength of repression increases as the target is moved toward the terminus and decreases as the target is moved toward the origin. In each case there is a small but reproducible 1.2–2  spike in repression when the target is located immediately proximal (B200 bp downstream) to the repressor gene. We encounter little interference from position-specific effects, with a few exceptions: in all cases, the target inserted & 2012 EMBO and Macmillan Publishers Limited

near the terminus at the essQ locus (see Supplementary Figure 1) remained unregulated. Additionally, when lacI-venus is inserted near the origin (Figure 6A) the repression strengths at essQ and nth near the terminus are significantly weaker than might otherwise be expected. This may be due to their location within the less densely packed chromosomal crossing region (Wiggins et al, 2010). These data were excluded from the best fit lines in Figure 6A–C.

Analysis and modeling: repression strength is inconsistent with a homogeneous TF distribution To understand these trends, it is necessary to model the response of the reporting promoter to its regulating TF. In steady state, the binding and unbinding of an operator by a TF Molecular Systems Biology 2012 7

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

Analysis and modeling: repression strength is consistent with local inhomogeneity

is described by the simple equilibrium equation ½TF þ ½O $ ½TF  O k

½TF½O : K¼ ½TF  O

ð2Þ

Consequently, at equilibrium any effects of TF-target intergenic spacing can be exerted only through the TF concentration, [TF], the concentration of the target operator, [O], and/or the equilibrium dissociation constant K. In Equation (2) the operator concentration, [O], changes due to the absolute location of genes relative to the replication origin. Because replication initiation and elongation occur from a single origin in E. coli, the period-averaged average gene copy number varies as a function of position according to ½Cð1  xÞ þ D/t

h½OðxÞi ¼ 2

ð3Þ

where C is the time to complete replication (40–70 min), D is the time lag between completion of replication and cell division (22–30 min), t is the doubling time of the culture, and x is the fractional location of the gene between the replication origin and terminus (origin at x ¼ 0 and terminus at x ¼ 1) (Cooper and Helmstetter, 1968; Helmstetter and Cooper, 1968; Bremer and Churchward, 1977; Bremer and Dennis, 1996). Because at the fastest growth rates reinitiation of replication occurs before the first termination, on average there can be as many as eight copies of origin-proximal genes for every one terminus-proximal gene. Increased intergenic spacing therefore leads to an imbalance of relative TF-target gene copy numbers if TF and target genes are located at disparate locations on the chromosome. To describe the repression data, we combine Equations (2) and (3) with a statistical mechanical model of transcriptional regulation of the promoter expressing lacZ (Buchler et al, 2003; Bintu et al, 2005a, b). For the promoter used in these experiments, we find that the repression strength, r, can be predicted as r¼1þ

½TF K

ð4Þ

(see Supplementary information—Promoter Modeling and Supplementary Figure 9). This model is used to fit the data in Figure 6. We first fit the data assuming a spatially homogeneous distribution of repressor (dashed colored lines in Figure 5A–C). The fits recapitulate the general trends: as the target is moved toward the terminus the ratio of average TF to target gene number increases, leading to increased repression strength. Conversely, when the target is moved toward the origin, the ratio of average TF to target gene number decreases, resulting in decreased repression strength. While these fits display the correct general trends, in all cases the strength of repression near the TF gene is B1.5  stronger than predicted by the null model. We note the similarity of this enhancement to the observed enhancement of LacI-Venus concentration summarized in Figure 2. According to Equation (4), r increases linearly with [TF] for this promoter; therefore, increases in TF concentration should result in corresponding enhancements in repression strength. 8 Molecular Systems Biology 2012

Keeping the microscopy results in mind, we next incorporate a local TF concentration gradient into our model. Since we assume that the gradient is generated by diffusion, and a steady-state diffusion gradient with constant linear degradation is exponential regardless of the details of the diffusion process (dimensionality, diffusion versus anomalous diffusion, etc.) (Hornung et al, 2005), we postulate a local exponential gradient that decays to a non-zero background concentration of repressor: ½TFðxÞ ¼ ½TF½1 þ g expð  j x  x0 j /lÞ

ð5Þ

where x0 is the location of the TF gene and x is the location in space where the concentration is being measured. The first term describes a constant background distribution of TF, while the second term describes a local exponential concentration gradient characterized by two additional parameters: a length scale l and a local enhancement factor g (we consider the origins of such a function in Discussion). Combining Equation (5) into our model and fitting the repression strength data yields the solid lines in Figure 6 and the fit parameters in Supplementary Table 2. In contrast to the fits assuming homogeneous repressor concentration, this model recapitulates the trends in the data as well as the local enhancement of repression near the TF gene. Given that KOid B0.1 nM (Oehler et al, 1994, 2006), the extracted TF concentrations are in the range of 0.1–14 nM (Gilbert and Muller-Hill, 1966); the smallest values can possibly be explained as a consequence of increasing K due to growth effects (see Supplementary information—Dilution and Growth Effects and Supplementary Figure 10).

Discussion The origins of TF inhomogeneity That steady-state TF concentration inhomogeneity can be observed at all is surprising given the small size of the cell and the time scales involved. In E. coli, TFs are produced from a localized source due to the persistent localization of mRNAs observed previously (Montero Llopis et al, 2010) and in this report and the spatial coupling of transcription and translation. Naı¨vely, as repressor diffuses away from this source, the shape of the resulting gradient should be determined by the ratio of the diffusion constant to the degradation rate of the TF (Ibanes and Izpisua Belmonte, 2008). The in vivo diffusion constant of LacI-Venus has been measured by live tracking of individual molecules to be B0.4 mm2/s (Elf et al, 2007), and the average time required for LacI-Venus to diffuse from one end of the cell to the other is therefore on the order of 1–10 s. The proteolytic degradation rate of LacI, on the other hand, is thought to be sufficiently small that dilution due to growth is generally assumed to be the primary mechanism for depletion (e.g., Narang and Pilyugin, 2008). That the dilution time scale is a minimum of 100–1000  slower than the diffusion time scale might lead one to expect that significant steady-state intracellular TF concentration inhomogeneity is impossible and that the intracellular TF concentration will rapidly homogenize. & 2012 EMBO and Macmillan Publishers Limited

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

From a physical point of view, the observed inhomogeneity of TFs can be explained only by a limited variety of mechanisms, and all of these mechanisms may be at play to some degree. One possibility is that the system could be heterogeneous as a transient state. This explanation appears to be ruled out as such transient states should be short lived based upon the known rates of diffusion observed by live tracking of individual molecules (Elowitz et al, 1999; Elf et al, 2007). However, since live tracking requires the maturation of fluorophores before they can be imaged (B10 min for Venus; Nagai et al, 2002; Elf et al, 2007), it is possible that there exist intranucleoid states immediately after TF production which diffuse anomalously or more slowly than heretofore reported. Another possibility is spatial heterogeneity of diffusion coefficients. However, this mechanism can only maintain inhomogeneity if there is localized production of TFs combined with degradation (Ibanes and Izpisua Belmonte, 2008; Wartlick et al, 2009). TFs are produced locally as a consequence of the persistent localization of mRNAs at the site of transcription (Montero Llopis et al, 2010) and the spatial coupling of transcription and translation. Under these conditions, the steady state resulting from localized production balanced with degradation, dilution, or nucleoid exclusion can lead to TF inhomogeneity within the nucleoid. Finally, spatial heterogeneity can be driven by spatial variation in energetic potentials for DNA, mRNA, and TFs, resulting in heterogeneity even at thermodynamic equilibrium. These spatial variations are almost certainly important here due to, e.g., the energetic favorability of TF-DNA binding and the observed exclusion of proteins from highly compacted DNA, perhaps driven by entropic mechanisms (Saberi and Emberly, 2010). We propose that the observed inhomogeneity is the result of competing forces of binding to DNA on one hand and exclusion from DNA on the other hand, and that the relative magnitude of these forces is dependent upon the local DNA compaction density. That the magnitude of the exclusion force is an increasing function of DNA density can be observed straightforwardly by examining the degree of exclusion of LacI42-Venus as a function of growth rate. With fast growth and low DNA density (last column in Figure 4), mutant LacI42Venus is not obviously excluded from the DNA volume. However, as growth rate decreases and compaction increases, exclusion increases until the mutant LacI42-Venus is more highly localized toward the ends of the cells in stationary phase (second column in Figure 3). These competing forces will influence the diffusive kinetics of TFs within the nucleoid. In steady state, we propose to describe intranucleoid diffusion by a mean-field model in which TFs can be separated into two sub-populations: those TFs confined within the nucleoid, [TF1], and those TFs undergoing 3D diffusion in the cytoplasm, [TF3]:

where a is the rate of TF production, b is the rate constant for degradation or dilution, D1 and D3 are the intranucleoid and extranucleoid diffusion coefficients, respectively, k1 and k2 are nucleoid exclusion and capture rate constants, respectively, and f is the fraction of TFs initially confined to the nucleoid after translation. We postulate that hops through 3D space of short duration within the nucleoid can be coarse grained along with true 1D sliding along DNA into effective 1D diffusion along the nucleoid. Only when TFs escape into the cytoplasm for an extended 3D excursion they are considered to be undergoing true 3D diffusion, and this escape is assumed to occur with linear rate constant k1 as a result of nucleoid exclusion forces. In this view, the escape rate constant k1 serves as the degradation rate constant of the nucleoidconfined sub-population. After escape, TFs diffusing in 3D rapidly form a homogeneous background pool and can be recaptured by the nucleoid with linear rate constant k2. A cartoon illustrating this argument is shown in Figure 7. The steady-state solution of a simplified 1D version of this model yields an enhancement of TF concentration around the encoding gene located at a position x0 (Kuhlman and Cox, in preparation): ½TFðxÞ ¼ ½TF½1 þ g expð  j x  x0 j /lÞ

ð7Þ

where x is the longitudinal distance from the source gene and we define the constants k2 af pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ½TF3 ; g  k1 ½TF D1 ðk1 þ bÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l  D1 /ðk1 þ bÞ

½TF 

ð8Þ

The solution (7) is precisely the functional form postulated in Equation (5), and has two terms: a constant background concentration [TF], and a local enhancement of concentration around the encoding gene whose magnitude relative to the background is characterized by the parameter g. This parameter is directly proportional to the fraction of TFs immediately captured by the nucleoid after translation, f. Thus, when the source of production is located within the nucleoid, f40, yielding non-zero g and localized

Cell wall Cytoplasm D1 D3

Homogeneous 3D pool Exclusion rate k1

Nucleoid

Capture rate k2

Effective D1 Repressor gene

q½TF1 ð~ x; tÞ ¼ af dð~ x ~ x0 Þ þ D1 r2 ½TF1   ðk1 þ bÞ½TF1  þ k2 ½TF3  qt q½TF3 ð~ x; tÞ ¼ að1  f Þdð~ x ~ x0 Þ þ D3 r2 ½TF3  qt  ðk2 þ bÞ½TF3  þ k1 ½TF1 

ð6Þ & 2012 EMBO and Macmillan Publishers Limited

Figure 7 A model of intranucleoid diffusion. TFs are produced at the site of the source gene within the nucleoid. TFs are initially confined to the nucleoid and diffuse via 1D sliding along the chromosome combined with short 3D hops between domains, which we coarse grain together as effective 1D diffusion along the entire nucleoid. TFs are excluded from the nucleoid with rate constant k1, where they quickly homogenize via rapid 3D diffusion to form a background pool of repressor. TFs can be recaptured into the nucleoid rate constant k2, and are diluted with rate constant b. Molecular Systems Biology 2012 9

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

inhomogeneity. When TFs are produced from an extrachromosomal source such as a plasmid directly into the cytoplasm, f ¼ 0, and this results in homogeneous distribution throughout the DNA, as observed experimentally (Figure 2). After production, it takes B10 min for the Venus fluorophore to mature (Nagai et al, 2002; Elf et al, 2007), a process that occurs even after fixation by paraformaldehyde (Little et al, 2011). Thus, we believe that our results remain consistent with previous live-tracking measurements of rapid intracellular TF diffusion (Elf et al, 2007) because live tracking requires the fluorophore to mature before it can be visualized. The nucleoid bound state leading to inhomogeneity, [TF1], may decay before maturation, and we argue that the cytoplasmic fraction [TF3], interacting with the nucleoid, may primarily be what was imaged in live-tracking experiments. The observations reported in this manuscript are in accord with previous reports regarding cis-acting proteins, such as the l-phage Q protein (Echols et al, 1976), the bacteriophage jX174 A protein (Francke and Ray, 1972), and the IS10 transposase of the Tn10 system (Morisato et al, 1983; Jain and Kleckner, 1993). These proteins have been shown to preferentially act upon closely located targets (Morisato et al, 1983; Jain and Kleckner, 1993), or to act only while synthesis is in progress, but cease to function later, even though intact and functional protein is still present (Echols et al, 1976). They are also generally DNA binding proteins, and their initial mechanism of action is similar to that of TFs such as LacI: the recognition of, and binding to, some cognate DNA sequence. This binding and unbinding will be governed by an equilibrium analogous to Equation (2), and we therefore suggest that the observed preferential cis-action may also be a consequence of protein inhomogeneity and concentration near the source gene. Furthermore, the activity of the IS10 transposase on transposons has been assayed as a function of the transposase/transposon intergenic distance (Morisato et al, 1983; Jain and Kleckner, 1993), and from an analysis of this data we find that this activity decays exponentially with distance, similar to that reported here with Lac repressor and modeled in Equations (5) and (7) (see Supplementary Figure 11). We also expect that the same rules of intranuceloid versus cytoplasmic production should influence the diffusive kinetics and spatial distribution of RNAs, and the results presented here may reconcile the apparent discrepancy between the observation of the rapid diffusion rates of RNAs (Golding and Cox, 2004; Golding et al, 2005) contrasted with the apparent colocalization of RNAs with chromosomally located source genes reported here and by Montero Llopis et al (2010). The rapid diffusion rates for RNAs observed by Golding and Cox resulted from quantitative measurement of RNAs produced from polar-localized bacterial artificial chromosomes; i.e., the RNAs were transcribed directly into the cytoplasm (f ¼ 0, Equation (6)). This is similar to the extrachromosomal plasmid reported here where it appears that the RNAs it produces have an enhanced tendency to redistribute compared with chromosomally produced RNAs (Figure 2; Supplementary Figure 5B). We might also expect that the diffusive kinetics of RNAs transcribed within the nucleoid are significantly different from those transcribed in the cytoplasm, and that the more crowded intranuceloid 10 Molecular Systems Biology 2012

environment will lead to slower rates of diffusion and a higher degree of RNA/gene colocalization.

Dynamic nucleoid organization as a regulatory strategy The observation that E. coli can dynamically alter the distribution of TFs and other intracellular proteins by changing the compaction state of its DNA may provide a mechanism by which E. coli can shift between global gene expression patterns. It has been previously demonstrated that E. coli generally reduces the expression of genes near the origin of replication and increases the expression of genes near the terminus upon DNA condensation (Berger et al, 2010). We note that since origin proximal genes lie within the body of the nucleoid and terminal-proximal genes lie within the loosely packed chromosomal crossing region which is exposed to the cytoplasm (Wiggins et al, 2010), these changes in gene expression correlate with the spatial changes in TF and protein distribution we observe during chromosomal condensation. Furthermore, we also observe reorganization and redistribution of DNA and protein upon exposure to serine hydroxamate, which induces the stringent response via amino-acid starvation (Ferullo and Lovett, 2008; Supplementary Figure 7B). We therefore suggest that protein redistribution driven by DNA condensation may be a general strategy for quickly altering global gene expression patterns in response to environmental stimuli, and, in particular, for sweeping non-specifically bound TFs from the DNA.

Implications for bacterial genome organization There is mounting evidence that the spatial organization of the prokaryotic genome is determined by the connectivity and coregulation of transcriptional regulatory networks, rather than through selection via horizontal gene transfer (Pa´l and Hurst, 2004; Warren and ten Wolde, 2004; Hershberg et al, 2005; Price et al, 2005; Kolesov et al, 2007; Wunderlich and Mirny, 2008; Janga et al, 2009; Yin et al, 2010). This work provides experimental evidence for a possible mechanism driving this organization. Because of the inhomogeneity of the intracellular TF concentration, gene targets are regulated more strongly and more quickly when located closer to their regulatory TF genes (Kolesov et al, 2007; Wunderlich and Mirny, 2008; Mirny et al, 2009). Because spatial distance is directly proportional to genomic distance (Wiggins et al, 2010), these regulatory benefits may provide selective pressure driving the close genomic organization of co-regulated genes on the bacterial chromosome.

Implications for eukaryotes Because eukaryotic TF proteins are not produced locally, transcriptional regulation of eukaryotic genes by TFs is not subject to the same effects of TF gene localization in bacteria that we focus upon here. However, the sites of nuclear reimportation serve as localized sources and may result in intranuclear TF inhomogeneity. This naı¨ve preconception may anticipate recent studies that reveal that some regulated genes & 2012 EMBO and Macmillan Publishers Limited

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

in yeast actively reorganize to the nuclear periphery and associate with nuclear pores upon exposure to inducing conditions (Ahmed and Brickner, 2007; Brickner et al, 2007; Ahmed et al, 2010).

were washed three times for 30 min each in wash buffer warmed to 301C. They were then rinsed once in 2  SSC and once in PBS, and finally mounted on glass slides with 40% glycerol.

Microscopy

Materials and methods Strains and plasmids All strains used in this study are derivatives of E. coli K-12 MG1655 Dlac (Kuhlman and Cox, 2010), in which the entire lac operon has been deleted from the N-terminus of lacI to the C terminus of lacA using the method of Datsenko and Wanner (2000). Strains with PlacI-lacI-venus::T1 (Nagai et al, 2002; Elf et al, 2007; Kuhlman and Cox, 2010) integrated at specific locations in the chromosome were constructed using Landing Pad technology as described previously (Kuhlman and Cox, 2010) and in Supplementary information. Required permissions for use of venus were obtained from Dr Atsushi Miyawaki at the Riken Brain Science Institute.

Media and growth conditions To obtain various doubling times, cells were grown at 371C in a shaking water bath with M63 medium (100 mM KH2PO4, 15 mM (NH4)2SO4, 1.7 mM FeSO4, 1 mM MgSO4) þ 0.5% glycerol, or Rich Defined Medium (Teknova) þ 0.5% glucose without antibiotics. We estimate that at the time of harvest cells had been growing in exponential steady state for B10 generations. Representative growth curves for each growth condition are shown in Supplementary Figure 2. A detailed protocol for cell growth can be found in Supplementary Information. For fixation, an equal volume of freshly prepared and filtered 5% paraformaldehyde in phosphate-buffered saline (PBS) was added directly to each culture. The resulting solution was allowed to continue shaking at 37 1C for 10 min and was then placed on ice for 30 min. Cells were washed three times via centrifugation and resuspension in 1 ml filtered, ice-cold PBS.

Fluorescent reporter-operator system Gene locations were determined using the FROS performed as described in Joshi et al (2011), the components of which were the kind gift of David Bates. Integrations were made at each site consisting of an array of 240 operators for tet repressor, TetR, using the Landing Pad technology. After growth to steady state as described above, 0.01% L-arabinose was added to each culture 1 h before fixation to induce expression of TetR tagged with fluorescent EYFP in trans from the plasmid pBH74 (Joshi et al, 2011). Cells were then fixed and processed as above.

Fluorescent in situ hybridization mRNA locations were determined by single-molecule FISH, performed as described in So et al (2011) using an array of 48 bp Stellaris FISH probes covering the coding sequence of lacI and labeled with CAL Fluor Red 590 purchased from Biosearch Technologies. Control experiments using similarly prepared probes for the coding strand of DNA yielded no bright spots, demonstrating specific labeling of mRNA. After fixation, cells in PBS were spread onto poly-L-lysine coated #1 22 mm  60 mm coverslips and allowed to adhere for 30 min. Coverslips were rinsed with PBS and soaked in 70% ethanol for 1 h to permeabilize the cell wall. The slides were then rinsed in wash buffer (40% formamide, 2  SSC buffer). In all, 100 ml of hybridization solution (40% formamide, 2  SSC buffer, 1 mg/ml E. coli tRNA, 200 mg/ml BSA, 2 mM ribonucleoside vanadyl complex, 2 ml of 2.5 mM probe stock) was added to each coverslip, which was then covered with two 22 mm  22 mm HybriSlip hybridization covers (Invitrogen). The coverslips were enclosed in watertight aluminum slide chambers and hybridized overnight in a 301C water bath. The next morning, slips

& 2012 EMBO and Macmillan Publishers Limited

After the appropriate preparation for the sample, the prepared coverslips were mounted on glass slides using 40% glycerol and, if appropriate, 5 mg/ml DAPI as a DNA stain. Nucleoid, FROS, and mRNA imaging were performed using a Nikon Eclipse TE2000U microscope with an Applied Scientific Instruments PZM-2000 automated stage utilizing Metamorph automation software. Images were gathered using epifluorescent illumination of the appropriate wavelength with a  100 phase contrast objective combined with a  4 telescope attachment using a Roper Scientific Cascade:512 camera. Single-molecule LacI-Venus microscopy was performed using a Nikon Eclipse TE2000U microscope with either a 488-nm laser (10 mW) or a 515-nm laser to improve the signal-to-noise ratio for LacI-Venus when needed, a TIRF microscopy attachment, and a Prior ProScan II automated stage using Andor iXon Basic software at  133 (for visual clarity in representative images) or  400 magnification (for image averaging). Emitted light was collected through the appropriate filter (ET 535/30 M) and the image captured by an Andor DV877-DCS-BV electron multiplying charge coupled device (EMCCD) camera. Imaging of the nucleoid with the same TIRF microscope after staining with SYBR green I (Invitrogen) yields the same average DNA distribution as that obtained with epifluorescent illumination of DAPIstained cells at all growth rates, indicating that the penetration depth of the evanescent TIRF wave is sufficiently deep to observe a volume representative of the entire nucleoid.

Data and image analysis All data and images were analyzed using custom software written in MATLAB 2010a (MathWorks). The distribution of LacI-Venus in each figure is determined as the difference in average spatial distribution of fluorescence in a LacI-Venus strain minus the average spatial distribution of autofluorescence of the same strain without the lacI-venus integration, grown under identical conditions. In particular, distributions obtained after the addition of chloramphenicol in Figure 5 were compared with samples of the negative control treated identically with chloramphenicol at each time point. Image analysis is discussed thoroughly in Supplementary Information—Image Analysis.

LacZ measurements For measurements of repression strength, the cells were grown as described above, and LacZ activity measured using traditional methods (Miller, 1972). When the density of the culture reached OD600 ¼ 0.2–0.4, a 0.5-ml sample of culture was added directly to 0.5 ml Z-buffer (Miller, 1972) and 40 ml chloroform (Fisher Scientific). Each sample was thoroughly mixed via repeated pipetting. In all, 200 ml of 4 mg/ml ortho-nitrophenyl-b-galactoside (ONPG; SigmaAldrich) in Z-buffer was added. When sufficient yellow color had developed to be visible by eye, 500 ml of 1 M Na2CO3 was added and the elapsed time recorded. OD420 and OD550 of each sample were measured in a spectrophotometer (Bio-Rad SmartSpec 3000) and the LacZ activity, a, was calculated as OD420  1:75OD550 2DtOD600 Repression strength, r, defined as a ¼ 1000

r ¼ a  /a þ

ð9Þ ð10Þ

and shown in Figure 6 is the ratio of the average of four measurements from independent cultures of each strain with (a þ ) or without (a  ) lac repressor. Error bars are calculated as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u   u X sai 2 ð11Þ sr ¼ hrit hai i i¼ þ/ Molecular Systems Biology 2012 11

Transcription factor distributions in E. coli TE Kuhlman and EC Cox

where sai are the standard deviations of the four measurements of a þ and a  .

Supplementary information Supplementary information is available at the Molecular Systems Biology website (www.nature.com/msb).

Acknowledgements We would like to thank Drs Sunney Xie and Atsushi Miyawaki for providing Venus constructs and the required permissions for their use; Dr David Bates for providing materials for FROS; and Drs Stephan Thiberge, Phuon Ong, and Bob Austin for assistance with microscopy. We would like to thank Justin Kinney, Simon Nørrelykke, Robert Cooper, Rob Phillips, Hernan Garcia, Terry Hwa, Ido Golding, Matthew Scott, Ned Wingreen, and Leonid Mirny for thoughtful discussions. This work was supported by the National Institutes of Health (GM078591, GM071508) and the Howard Hughes Medical Institute (52005884). TEK is supported by an NIH Ruth Kirschstein NRSA Fellowship (F32GM090568-01A1). Author contributions: TEK and ECC designed experiments and wrote the paper. TEK performed all strain construction, experiments, modeling and analysis.

Conflict of interest The authors declare that they have no conflict of interest.

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